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Suppose your neighbor's kid comes by to offer you a lottery ticket for the school fundraiser. There are 700 tickets sold and each ticket costs 10. The prizes are as follows: 1st ticket drawn =500, 2nd ticket drawn = 250, 3rd ticket drawn =100. If all 700 tickets are sold, what is your expected value if you buy a ticket?

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Final answer:

The expected value of buying one $10 lottery ticket with 700 sold in total, where prizes are $500, $250, and $100, is an expected loss of $8.785 per ticket.

Step-by-step explanation:

To calculate the expected value when buying a ticket in the school fundraiser, we consider the probability of winning each prize and its corresponding value. With 700 tickets sold, there is a 1/700 chance to win the first prize of $500, a 1/699 chance to win the second prize of $250 (since one ticket has been removed), and a 1/698 chance to win the third prize of $100 (after removing two tickets). The expected value is computed as follows:

  • Expected value for 1st prize: (1/700) × $500 = $0.714
  • Expected value for 2nd prize: (1/699) × $250 = $0.358
  • Expected value for 3rd prize: (1/698) × $100 = $0.143

The combined expected value from prizes is $0.714 + $0.358 + $0.143 = $1.215.

Since each ticket costs $10, the net expected value is the expected winnings minus the cost of the ticket:

Net expected value = Expected winnings - Cost of ticket = $1.215 - $10 = -$8.785.

Therefore, you would expect to lose $8.785 on average for each ticket purchased. This is your expected loss per ticket.

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